Theorem hvaddcl

Description: Closure of vector addition. (Contributed by NM, 18-Apr-2007) (New usage is discouraged.)

	Ref	Expression
Assertion	hvaddcl	⊢ ( ( 𝐴 ∈ ℋ ∧ 𝐵 ∈ ℋ ) → ( 𝐴 +ℎ 𝐵 ) ∈ ℋ )

Proof

Step	Hyp	Ref	Expression
1		ax-hfvadd	⊢ +ℎ : ( ℋ × ℋ ) ⟶ ℋ
2	1	fovcl	⊢ ( ( 𝐴 ∈ ℋ ∧ 𝐵 ∈ ℋ ) → ( 𝐴 +ℎ 𝐵 ) ∈ ℋ )